I'm not sure about that- in my experience I've always found airsoft more painful than paintball at a normal skirmish level. I'm sure 'speedball' or whatever it is hurts more than normal paintball, but there's an equal amount of pain no matter what type of skirmish, be it a milsim or a normal turn up day.
As well as this, BBs only have a few mm that hits you, meaning that over a joule of force is being transmitted to your skin in a very small area.
In general paintballs seem to fly at a much lower velocity, and the low force from a paintball is felt in a much larger area.
This means that the force from a paintball hitting your arm will be displaced over a larger area and the feeling will be less intense than a BB hitting you with much more force over a smaller surface area.
A good analogy for this would be the cork board pressure/surface area link. If you took a pin and a bolt and applied the same amount of force onto the corkboard through them, the pin would go in and the bolt wouldn't. This is because the head of the pin has a smaller surface area than the face of the bolt, so more pressure is applied over a smaller area meaning less force is displaced.